Reduced Whitehead groups and conjugacy problem for special unitary groups of anisotropic hermitian forms

Let $K/k$ be a separable field extension of degree 2, $D$ be a finite-dimensional central division algebra over $K$ with $K/k$-involution $\tau$, $h$ be an hermitian anisotropic form on a right $D$-vector space with respect to $\tau$ and let $U(h)$ be the unitary group of $h$. Then the reduced Whitehead group of its special linear subgroup is defined as follows: $\mathrm{SUK_1^{an}}(h)=\mathrm{SU}(h)/[U(h),U(h)]$, where $[U(h),U(h)]$ is the commutator subgroup of $U(h)$. The first main result establishes a link between the above group and its analog $\mathrm{SUK}_1(h)$ for the case of isotropic $h$ (with respect to the same $\tau$).
Theorem. There exists a surjective homomorphism from $\mathrm{SUK_1^{an}}(h)$ to $\mathrm{SUK}_1(h)$.
Furthermore, we give also a solution of conjugacy problem for special unitary subgroups of anisotropic hermitian forms over quaternion division algebras as subgroups of their multiplicative groups.